What's the difference between a 'skill' in Claude for Chrome versus a skill in Claude Desktop?

One member's understanding is that Claude for Chrome has more ability to take actions in the browser (described as more ability to 'do bad things') compared to Claude Desktop. Because of this, one participant said they keep the web-browsing capability turned off in their Claude for Chrome setup so it can't act on the web, and are working in a locked-down way until they build more trust in the tool. This was described as still being worked out, not a definitive technical answer.